The Laplace approximation [1]}, [2]} is an integral part of our proposed solution. In the context of Bayesian neural networks, we seek the weight-posterior \(p(\theta | \mathcal {D}) \propto \exp (-\mathcal {L}(\mathcal {D}; \theta ))\) , where \(\theta \)  are network weights, \(\mathcal {D}\)  is the training data, and \(\mathcal {L}\)  is the applied loss function interpreted as an unnormalized log-posterior. This is generally intractable and Laplace's approximation (la) amounts to a second-order Taylor expansion around a chosen weight vector \(\theta ^*\)
\(\log p({\theta }| \mathcal {D})& = \mathcal {L}^*+ ({\theta }- {\theta }^*)^{\top } \nabla \mathcal {L}^*+ \frac{1}{2} ({\theta }- {\theta }^*)^{\top } \nabla ^2 \mathcal {L}^* ({\theta }- {\theta }^*) + \mathcal {O}(\Vert {\theta }- {\theta }^*\Vert ^3)\) 
